The equation of a line is given as:
y = mx + c
where the slope is m and c is the constant of proportionality.
The coordinates of a point on the line has been given to us as (2, -1) i.e. x = 2 and y = -1.
The only thing unknown to write the equation of the line is the constant C.
Therefore, in order to get C, we should substitute the values of x, y and m into the equation of the line:
y = mx+ C
[tex]\begin{gathered} y=mx+c \\ y=-1,x=2,m=\frac{3}{4} \\ -1=\frac{3}{4}\times2+c \\ -1=\frac{3}{2}+c \\ \text{subtract }\frac{3}{2}\text{ from both sides} \\ -1-\frac{3}{2}=c \\ c=-\frac{5}{2} \end{gathered}[/tex]Now that we have the value of c, we can proceed to write the equation as:
[tex]\begin{gathered} y=\frac{3}{4}x+-\frac{5}{2} \\ y=\frac{3}{4}x-\frac{5}{2} \\ \\ \text{Multiply both sides by 4} \\ 4\times y=4\times(\frac{3}{4}x-\frac{5}{2}) \\ 4y=4\times\frac{3}{4}x-4\times\frac{5}{2} \\ 4y=3x-10 \\ rearrange\text{ the equation} \\ 3x-4y=10 \end{gathered}[/tex]Therefore the final answer is: 3x - 4y = 10 (A)
